Abstract. A binary stream cipher, known as A5, consisting of three short LFSRs of total length 64 that are mutually clocked in the stop/go manner is cryptanalyzed. It is allegedly used in the GSM standard for digital cellular mobile telephones. Very short keystream sequences are generated from different initial states obtained by combining a 64-bit secret session key and a known 22-bit public key. A basic divide-and-conquer attack recovering the unknown initial state from a known keystream sequence is first introduced. It exploits the specific clocking rule used and has average computational complexity around 2 40 . A time-memory trade-off attack based on the birthday paradox which yields the unknown internal state at a known time for a known keystream sequence is then pointed out. The attack is successful if T · M > 2 63.32 where T and M are the required computational time and memory (in 128-bit words), respectively. The precomputation time is O(M) and the required number of known keystream sequences generated from different public keys is about T/102. For example, one can choose T ~ 2 27.67 and M ~ 2 35.65 . To obtain the secret session key from the determined internal state, a so-called internal state reversion attack is proposed and analyzed by the theory of critical and subcritical branching processes. Document Classification unclassified Classification of SF298 unclassified Classification of Abstract unclassified Limitation of Abstract unlimited Number of Pages 21 REPORT DOCUMENTATION PAGE Form Approved OMB No. 074-0188Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to
In this paper, we introduce a family of games called concave pro-rata games. In such a game, players place their assets into a pool, and the pool pays out some concave function of all assets placed into it. Each player then receives a pro-rata share of the payout; i.e., each player receives an amount proportional to how much they placed in the pool. Such games appear in a number of practical scenarios, including as a simplified version of batched decentralized exchanges, such as those proposed by Penumbra. We show that this game has a number of interesting properties, including a symmetric pure equilibrium that is the unique equilibrium of this game, and we prove that its price of anarchy is Ω(n) in the number of players. We also show some numerical results in the iterated setting which suggest that players quickly converge to an equilibrium in iterated play.
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